RMS speed, degrees of freedom and equipartition - One Line Questions

1. For a monatomic gas molecule, what is the number of degrees of freedom? — 3
2. A triatomic linear molecule (like CO2) has how many degrees of freedom related to vibration? — 2
3. The ratio of specific heats (Cp/Cv) for a diatomic ideal gas at moderate temperatures is approximately: — 1.40
4. The ratio of specific heats (Cp/Cv) for a monatomic ideal gas is known as the adiabatic index, γ. What is its value? — 1.67
5. If the temperature of a gas is increased by 2 K, the increase in its average kinetic energy per molecule is: — 2k
6. The number of degrees of freedom for translational motion is always: — 3
7. A diatomic molecule typically has how many degrees of freedom at moderate temperatures? — 5
8. What is the average kinetic energy of one molecule of an ideal gas at absolute temperature T? —
9. According to the equipartition theorem, the average energy associated with translational motion for a molecule is: — 3/2 kT
10. What is the specific heat at constant volume (Cv) for a monatomic ideal gas per mole? — 3/2 R
11. For a monatomic gas, the internal energy per mole is: — 3/2 RT
12. The ratio of RMS speed of hydrogen molecules to that of oxygen molecules at the same temperature is: — 4:1
13. At very high temperatures, a diatomic molecule can have how many degrees of freedom? — 7
14. The average kinetic energy of a diatomic molecule at temperature T is approximately: — 5/2 kT
15. For a diatomic molecule in thermal equilibrium, the total average internal energy per molecule is: — 5/2 kT
16. What is the specific heat at constant volume (Cv) for a diatomic ideal gas per mole at moderate temperatures? — 5/2 R
17. A non-linear triatomic molecule has how many degrees of freedom at moderate temperatures? — 6
18. What is the value of the universal gas constant (R)? — 8.314 J/mol·K
19. The kinetic energy of a gas is directly proportional to: — Absolute temperature
20. The average translational kinetic energy of gas molecules is directly proportional to: — Absolute temperature
21. At higher temperatures, the contribution of vibrational modes to the specific heat of a diatomic gas becomes significant. This leads to: — An increase in Cv
22. The equipartition theorem is a consequence of: — Classical mechanics
23. The specific heat capacity of a gas depends on: — Degrees of freedom
24. What does the equipartition theorem state? — Each degree of freedom of a molecule contributes 1/2 kT to its average energy
25. The average energy of a photon in black body radiation is given by kT. This is an example of: — Equipartition theorem
26. If a gas has f degrees of freedom, its molar specific heat at constant volume is given by: — f/2 R
27. Which gas will have the lowest RMS speed at 27°C? — Krypton (Kr)
28. If the volume of a gas is kept constant, and its temperature is increased, the RMS speed of the molecules: — Increases
29. If the temperature of a gas is increased, the collision frequency of the molecules: — Increases
30. If the absolute temperature of a gas is doubled, how does its RMS speed change? — It increases by a factor of sqrt(2)
31. Which statement is incorrect regarding the RMS speed of gas molecules? — It is directly proportional to the pressure.
32. What is the unit of Boltzmann constant (k)? — Joule per Kelvin (J/K)
33. For a diatomic molecule, vibrational degrees of freedom contribute how much energy per molecule according to equipartition theorem? — kT
34. For a rigid diatomic molecule, rotational degrees of freedom contribute: — kT
35. In the equation v_rms = sqrt(3kT/m), what does 'm' represent? — Mass of a single molecule
36. In the formula for RMS speed, v_rms = sqrt(3RT/M), what does 'M' represent? — Molar mass of the gas
37. For a monatomic gas, Cp - Cv = R. For a diatomic gas, Cp - Cv is also R. This is an application of: — Mayer's relation
38. Which type of gas molecule has the maximum number of degrees of freedom at room temperature among monatomic, diatomic, and triatomic (linear)? — Triatomic (linear)
39. Which of the following gases will have the highest RMS speed at a given temperature? — Hydrogen (H2)
40. The adiabatic process is described by PV^γ = constant. What does γ represent? — Ratio of specific heats (Cp/Cv)
41. If the pressure of an ideal gas is doubled while keeping the temperature constant, the RMS speed of its molecules will: — Remain unchanged
42. The internal energy of an ideal gas depends only on: — Temperature
43. The RMS speed of gas molecules is independent of: — Number of molecules
44. The mean free path of gas molecules depends on: — Molecular diameter and number density
45. What is meant by the 'degrees of freedom' of a molecule? — The number of ways a molecule can move
46. What is the RMS speed of gas molecules directly proportional to? — The square root of its absolute temperature
47. The equipartition theorem applies to systems in: — Thermal equilibrium
48. The equipartition theorem is applicable under which condition? — Thermal equilibrium
49. Which of the following is NOT a degree of freedom for a molecule? — Intermolecular attractive force
50. The RMS speed of gas molecules is given by the formula: — v_rms = sqrt(3RT/M)
All One Line Questions
E-Book RMS speed, degrees of freedom and equipartition Online Test RMS speed, degrees of freedom and equipartition Question Bank RMS speed, degrees of freedom and equipartition